This invention is in the field of split-cycle Stirling-cycle coolers which generally have a compression portion and expansion portion connected by a refrigerant conduit. The expansion portion has a "cold finger" in which expansion of the refrigerant occurs. This cold finger has an ambient end from which the refrigerant flows towards a cold end. Thus a temperature gradient exists from the ambient to the cold end of the finger. Typical of such coolers are those shown in the U.S. Pat. Nos. 3,630,041, 3,862,546, and 3,877,239. An improvement in operation of such typical coolers could be realized if the temperature gradient along the cold finger were reduced. The present invention is able to reduce this gradient by providing a cooling stage for the ambient end of the cold finger.